The objective of this work is to relate the specificities of antibodies, antigens and genes to the data observed in histocompatibility reaction matrices or tables. The definition problem is the problem of (operationally) defining single antigen and antibody species by their specificities. Observed data displayed in a reaction matrix is the result of reactions between combinations of (i.e., sets of) antigens and antibodies. Both antigens and antibodies may be crossreacting. The labeling problem is the problem of labeling the rows and columns of the given matrix with sets of antigen and antibody species in such a way as to produce the observed reaction pattern when specificities are given by the definition. Labeled reaction matrices (LRM) are discrete deterministic mathematical models developed by the principal investigator to solve the definition and labeling problem. It is proposed to further develop the theory of LRM and to generalize the concept in order to model several mechanisms and notational languages describing the data in a histocompatibility matrix in terms of basic antigen antibody reactions.